Find x for ln x=-2 using the natural logarithm formula

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In summary, for the equation ln x = -2, the value of x can be found by using the formula x = e^-2, which is approximately 0.135. However, this only applies for the real number version of the ln function, where the domain is positive real numbers and the range is all real numbers. For ln(-2), a complex version of the function would need to be used.
  • #1
justin345
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lnx=-2 ---- find x

Homework Statement



Hi!
We know that ln x=y, thus x=e^(y).
If I have ln x=-2, can my x be equal e^(-2)=0.135?
 
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  • #2


justin345 said:

Homework Statement



Hi!
We know that ln x=y, thus x=e^(y).
If I have ln x=-2, can my x be equal e^(-2)=0.135?
Yes, ln x = -2 <==> x = e-2, which is approximately 0.135.
 
  • #3


I am asking because for negative natural logs, there is a more complicated formula with sin and cos and Pi.
So you are saying that it is okay to use this one? Thank you!
 
  • #4


No, I'm not saying that at all. For the real number version of the ln function, the domain is positive real numbers, and the range is all real numbers.

If you had ln(-2), that would be a different matter altogether, and you would need the complex version of this function.
 

FAQ: Find x for ln x=-2 using the natural logarithm formula

What is Lnx?

Lnx is a mathematical expression that represents the natural logarithm of x. It is commonly written as ln(x) or loge(x).

What does the equation Lnx=-2 mean?

This equation means that the natural logarithm of x is equal to -2. In other words, -2 is the power to which the base of the natural logarithm (e) must be raised to get x.

How do I solve for x in the equation Lnx=-2?

To solve for x, we need to use the inverse of the natural logarithm function, which is e^x. We can rewrite the equation as e^x = e^-2 and then take the natural logarithm of both sides to get x = -2.

Can the equation Lnx=-2 have more than one solution?

Yes, the equation can have multiple solutions, as the natural logarithm function is not a one-to-one function. This means that different values of x can result in the same output of -2.

What is the significance of the equation Lnx=-2 in mathematics or science?

The equation Lnx=-2 is commonly used in calculus and other fields of mathematics and science to solve for unknown variables in exponential and logarithmic functions. It is also used in modeling and analyzing natural phenomena, such as population growth and decay.

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